First of all, you really shouldn't worry about the forecasts. Current forecasts are absolutely unreliable for mid-June. They'll start to make sense only a couple of days in advance. Please find further information here.

As for your questions:

1. Yes, if flexibility is important to you it's wise to get a Swiss Travel Pass. Please find purchase options here.

2. Yes, additional tickets can be bought at the spot. Seat reservations aren't necessary, except for some panoramic trains such as the Glacier Express. Although June isn't the tourist peak season yet, you may want to consider arranging for this in advance too, as it's quite a popular train.

3. Two mountains in one day should be doable. It's all about your personal preferences. You can check schedules with the aid of the general timetable and the information under the "Route" tabs on our attraction pages, e.g. Rigi, Pilatus, Titlis and Stanserhorn. You'll find links to separate mountain transportation timetables on these pages too. If you don't mind long traveling days and think your baby is up for it, it's all fine. Do remember to be cautious when bringing your infant up to high altitudes, as altitude sickness may pose problems. Information is at our attraction pages, e.g. our Titlis page.

Happy to hear our website has been useful so far! I'd avoid trying to visit three mountain tops in one day indeed; two is definitely enough. Titlis and Rigi require most traveling time in all from Lucerne, so I'd do both on separate days and then add either Stanserhorn or Pilatus.

Great that you get to visit France and Austria too! I hope you'll enjoy your Europe trip.